What is Presentation of a monoid?

In algebra, a presentation of a monoid is a description of a monoid in terms of a set Σ of generators and a set of relations on the free monoid Σ generated by Σ. The monoid is then presented as the quotient of the free monoid by these relations. This is an analogue of a group presentation in group theory.

As a mathematical structure, a monoid presentation is identical to a string rewriting system. Every monoid may be presented by a semi-Thue system.

A presentation should not be confused with a representation.